Agree with bob here.
The only perceived advantage I can see of using a Mullard or other NOS type is that if you are pushing it hard, the newer versions don't seem to be up to the higher current draws. Larger Leak Stereo Amps spring to mind here, the Stereo50 and 60 with EL34 valves. The stereo 20., TL12+, and other TL models would be fine with a chenes or east european GZ34.
I now use a Golden Dragon GZ34 in my Stereo20 and it hasnt gone pop on me yet. Unlike the original Mullard GZ34 that failed in a most spectacular fashion.
The other upside as bob has pointed out, is the cost. Even used GZ34 command crazy money prices now.
Does it have to be a GZ34? If you have enough current capacity on the 5V heater windings then something like a 5U4G might work, being aware of the almost instant warm up time, lower max first capacitor values, and increased voltage drop.
Andy.

The Sovtek 5AR4 is a very good new production alternative. I prefer it by a wide margin to the JJ GZ34. For less demanding applications the Mullard GZ30 (CV2748) is a much more affordable option than the GZ34. And let's not forget the excellent (and not too pricey) Chatham JAN 5R4 WG "potato masher", which was reportedly used in B52 bombers and is directly heated like the 5U4G.

I have been surprised, down the years trying all sorts of direct and indirectly heated rectifiers, that there appear to be sonic differences... (Going off piste, I most love mercury vapour rectifiers - they look wicked and have interesting properties that ordinary rectifiers just don't have.) I have found the potato mashers to be an abomination; the Sovtek GZ34 is solid and reliable as the JJ GZ34 is a firework in a glass envelope. Mullard GZ34s are superb having tried and used them in many places. I wouldn't bother with a guitar amp but with several SE valve amps from Ongaku down to little 71 or 45 jobbies the Mullard GZ34 shines where others merely work.

I have not explored their use in PP amps but just used a Mullard in a Leak stereo amp because I could, at the time.

All imho (but from quite a lot of experience actually) If I'm starting from scratch with a build I use 6DS22s - superb and oh so cheap!